Hello tsaitea. Welcome to PF !tsaitea said:lim e^(1/(6-x))
x->6+
Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.
Actually [itex]\displaystyle \ \ \lim_{x\to6^{+}}\,\frac{1}{6-x}=-\infty\ . [/itex]tsaitea said:oh -infinity, but the answer is e^(17/3)?, maybe the book is wrong then?
A one-sided limit is a mathematical concept that describes the behavior of a function as its input approaches a specific value from either the left or the right. It is used to determine if a function is approaching a particular output value from a particular direction.
A one-sided limit only considers the behavior of a function from one direction, either the left or the right, while a two-sided limit considers the behavior of a function from both the left and the right. This means that a function can have different one-sided limits at a specific point, but only one two-sided limit.
One-sided limits are important because they can help us determine if a function is continuous at a specific point. If both the left and right one-sided limits are equal to the function's output at that point, then the function is continuous at that point. They are also useful in finding vertical and horizontal asymptotes of a function.
To calculate a one-sided limit, we need to evaluate the function as the input approaches the specific value from the given direction. This can be done by plugging in values that are very close to the specific value from the desired direction and seeing if the function output approaches a particular value.
Yes, a function can have one-sided limits but not a two-sided limit. This can occur when the function approaches a different output value from the left and right sides of a specific point, meaning that the two-sided limit does not exist. However, the one-sided limits may still exist and be different from each other.